Monday, November 26, 2018

Kelly's Multiple Personality Disorder

For the professional sports-trader, Kelly has three separate mathematical forms:
  1. Single Event, Single Selection;
  2. Single Event, Multiple Selections; and
  3. Multiple Events, Multiple Selections.

Single Event, Single Selection

This is the basic case as outlined in cursory descriptions of the Kelly Criterion. We identify a selection, which gives us an edge over the market and calculate the optimal stake to maximize that advantage. For this purpose, the Excel Add-In offers the KellySingleStake sports-trading function that accepts Decimal OddsWin Probability, and Multiplier parameters. The KellySingleStake function is the correct formula for AvB events such as moneyline markets in MLBNBA, and the NFL.

Decimal OddsWin ProbabilityStake
2.0053%6.00%

Single Event, Multiple Selections

In AvB events, the general advice to only bet the overlay is technically correct. However, in an AvK event, such as horse-racing and golf with a number of mutually-exclusive outcomes this advice is not strictly correct. Kelly betting is predicated on maximizing the logarithm of the handicapper's bankroll over the long-term. But, in the short-term, that goal is translated into not losing specific events when the price is right! The key role played by overlays in mutually-exclusive events is that there must be at least one such betting option available in any event on which we wish to bet. Beyond that, the specific choices will only be governed by maximizing the logarithm of our bankroll! The sports-trading function, KellyMutExStakes (array formula), with Decimal Odds Range and Win Probability Range inputs will identify the optimal selections and stakes.

EntryDecimal OddsWin ProbabilityTrader EdgeStake
Charlie5.5020.00%10.00%5.96%
Alpha2.62540.00%5.00%10.59%
Bravo3.2530.00%-2.50%6.25%
Delta6.008.00%-52.00%0.00%
Echo21.002.00%-58.00%0.00%

Multiple Events, Multiple Selections

For Nx(AvB) events, such as trading Ryder Cup golf singles matches or NFL games on Any Given Sunday, we need the sports-trading function, KellySimEvtStakes (array formula), with Decimal Odds Range and Win Probability Range parameters to identify the optimal stakes.

EntryDecimal OddsWin ProbabilityTrader EdgeStake
SvWH1.5075.00%12.50%9.10%
BHAvB1.4080.00%12.00%11.70%
DvAV1.6070.00%12.00%6.825%
LvCP1.3085.00%10.50%14.70%
AvB1.000.00%-100.00%0.00%

Note that Example #2 in the Pinnacle Guest article - The real Kelly Criterion - calculates the wrong stakes as can easily be confirmed by entering the decimal odds and win probabilities into the SBR Kelly Calculator for four independent events.